well, i love Rainbow because their songs are good especially the older ones...and they're decent singers and they don't have any fake pretentious personalities and are carefree and act like ahjummas sometimes but many hate them anyway i guess for the same reason...they don't pretend to be goody girls and they're just jealous.
another one i'd suggest, Nine Muses, they started out being hated by everyone for no reason but made their way up and now i think many who knows them like them. like Rainbow, they're solid performers/singers, although the changes in their lineup may cause confusion
both groups are more towards y concepts....not really trashy though i'd say.
there are more girlgroups i like, like KARA(i really adore their debut time, especially when they had 4 members), Brown Eyed Girls(honestly i prefer their music when they're not idol-fied...they used to be just music centered), Rania(if you don't hate y concept...though i stop following them after 2nd single)...there are a few more i like but mostly have disbanded like Storm(really badass), JQT(great live perfs), Lady Collection(well, i just like one member but their music n vocals are really good) etc.
Sorry i can't suggest current/new ones cuz none attract my attention. lol.

Orange Caramel